Connections to Gaussian processes
Hover over the links for details on some connections. Dots indicate ‘special cases of’. Undirected connections suggest equivalence or a more complex relationship. Note this is for a quick reference, not an exhaustive one.
Matern class
Note that covariance functions are written identically in slightly different ways in different sources, and this is just one representation. See the Rasmussen and Williams link for details.
\[h^2\frac{2^{1-\nu}}{\Gamma(\nu)}(2\sqrt{\nu}\frac{|x_i-x_j|}{\lambda})\mathcal{B}_\nu(2\sqrt{\nu}\frac{|x_i-x_j|}{\lambda})\]
- \(\lambda\) = horizontal/input length-scale
- \(h\) = vertical/output length-scale
- \(\nu\) = controls differentiability
- \(\Gamma\) = Gamma function
- \(\mathcal{B}\) = modified Bessel function
Labels
- GP = Gaussian process
- Matern = Matern covariance structure
- Exp = exponential covariance structure \(h^2\exp(-\frac{|x_i-x_j|}{\lambda})\)
- SqExp = squared exponential covariance structure \(h^2\exp[-(\frac{|x_i-x_j|}{\lambda})^2]\)
- RQ = rational quadratic covariance structure \(h^2(1 + \frac{|x_i-x_j|^2}{\alpha\lambda^2})^{-\alpha}\)
- Other = other covariance functions
- OU = Ornstein-Uhlenbeck process
- GAM = generalized additive models
- Splines = piecewise polynomial, regression splines
- SVM = support vector machines
- NN = neural networks